-1 of 3

A test for a particular illness that affects 8% of the general population has the following properties:

• The test will show a positive in 95% of cases where the patient has the illness and a negative in 5% of such cases.
• The test will show a false positive in 5% of patients who do not have the illness and a negative result for 95% of patients who do not have the illness.

Note that a positive result means that the test indicates that the patient has the illness. A negative result means that the test indicates that the patient doesn't have the illness.

A patient has just been tested and shows a positive result. Assuming all other things being equal, and based on the above information, find the probability that the patient has the illness. Give your answer as a decimal to 2 decimal places.

Probability that patient has illness =______

-2 of 3

During an international flight, a pilot notices a warning light come on somewhere on the panel. The light indicates that one of the landing wheels is not fully functional. The pilot reasons that this may mean that there is actually a problem with the wheel, however it may also mean that the warning light itself is malfunctioning. There are back-up wheels for this sort of situation, but the pilot would still like to know whether or not the wheel is fully functional.

The pilot, who is very experienced with the mechanical and technical specifications of the plane, knows the following probabilities:

• There is only ever a problem with a wheel in 3 out of every 1,000 flights. That is, the probability of there being a problem with a wheel on any given flight is 0.003.
• The warning light is very accurate when it comes to positively reporting a problem. Specifically, if thereisa problem with one of the wheels, the probability that the warning light will come on is 1.
• However, the warning light also occasionally comes on even if there is no problem - although this is extremely rare. The probability that the light will come on during a flight when thereisn'ta problem is 0.0002.

Based on this information, calculate the probability that there isnota problem with a wheel given that the warning light has just come on for the pilot. Give your answer as a decimal to 3 decimal places.

P(there is not a problem|warning light is on) =__________

-3 of 3

In the Legal Eagle law firm, 77% of the lawyers are male while 23% are female. Of the male lawyers, 36% are corporate lawyers and 64% are non-corporate lawyers. Of the female lawyers, 25% are corporate lawyers and 75% are non-corporate lawyers.

If a lawyer is chosen at random and they arenota corporate lawyer, calculate the probability that they are female. Give your answer as a decimal to 2 decimal places.

Probability =________